The invention relates to shaving systems having handles and replaceable blade units. Shaving systems often consist of a handle and a replaceable blade unit in which one or more blades are mounted in a plastic housing. Such shaving systems often include a pivoting attachment between the blade unit and handle, which allows the blade unit to maintain optimum contact with the surface being shaved. The pivoting attachment often includes a mechanism to provide resistance during shaving and return the blade unit to a neutral or “rest” position when it is not in contact with the user's skin.